Multiply. Write the result in the form a + bi.
-$( 2 + \sqrt { - 2 } ) ( 4 + \sqrt { - 2 } )$
A) $( 8 - \sqrt { 4 } ) + ( 2 \sqrt { 2 } + 4 \sqrt { 2 } ) \mathrm { i }$
B) $4 - 6 \sqrt { 4 } i$
C) $( 8 + \sqrt { 4 } ) - 12 i$
D) $12 + 24 \mathrm { i }$

Question

Quizplus · Accepted Answer

Multiplying the given complex numbers $(2 + \sqrt{-2})$ and $(4 + \sqrt{-2})$, we use the distributive property (FOIL method) to expand the expression: $2*4 + 2*\sqrt{-2} + \sqrt{-2}*4 + \sqrt{-2}*\sqrt{-2}$. This simplifies to $8 + 2\sqrt{-2} + 4\sqrt{-2} - 2$ (since $\sqrt{-2}*\sqrt{-2} = -2$). Combining like terms, we get $6 + 6\sqrt{-2}i$, which can be rewritten as $6 + 6i\sqrt{2}$, matching the form of choice A after recognizing a simplification error in the explanation but correctly identifying the structure of the answer.

Multiply Write the Result in the Form a + Bi (2+−2)(4+−2)( 2 + \sqrt { - 2 } ) ( 4 + \sqrt { - 2 } )(2+−2​)(4+−2​)

Multiply Write the Result in the Form a + Bi $( 2 + \sqrt { - 2 } ) ( 4 + \sqrt { - 2 } )$